Fluorescence spectrum and thermalization in a driven coupled cavity array

We calculate the fluorescence spectra of a driven lattice of coupled cavities. To do this, we extend methods of evaluating two-time correlations in infinite lattices to open quantum systems; this allows access to momentum-resolved fluorescence spectrum. We illustrate this for a driven-dissipative transverse-field anisotropic XY model. By studying the fluctuation-dissipation theorem, we find the emergence of a quasithermalized steady state with a temperature dependent on system parameters; for blue-detuned driving, we show this effective temperature is negative. In the low excitation density limit, we compare these numerical results to analytical spin-wave theory, providing an understanding of the form of the distribution function and the origin of quasithermalization.